From: Utlima Thule
Well if it still all went tits up - despite all having roughly the same religion - then at least we wouldn't have the divided island (I assume) and all the carnage that brought?
Sadly my knowledge of this part of history (1600-1915) and what was really going on in the three Kingdoms, isn't sufficiently strong to have any real sense of what may or may not have been possible.
I'm not sure you can say much, since the divide between Catholicism, Anglicism and the Church of Scotland was not really theologically driven, you can assume those 3 stay broadly united and claim the religious allegiance of most inhabitants of England, Scotland and Ireland.
You then have the various non-comformist protestant groups, probably stronger as there is no anglicanism to draw off their less committed adherents.
So this GB follows the European norm? A political clash between an absolutist royal philosophy, a rising merchant and farming class that wants political involvement in return for its tax monies and no doubt unhappy peripheral regions (Highlands/Ireland but also possibly N England).
Well no European state navigated say 1600-1800 without a lot of internal angst, and there are a lot of ways those dynamics could have fallen out. We can assume that an international level relations with France, Spain and the Netherlands would have been as tricky, that this GB would have intervened in continental wars for tactical gains and those powers would have returned the favour.
The Stuarts were mostly spectacularly inept, but the pressures on them are different. And you don't have the ready triangle of Anglican/Catholic/Non-Comformist that maps so easily onto what we know happened (since we are living with the consequences). Without the Anglican/Catholic dynamic Ireland might have been less consistently rebellious but then, in Scotland, that divide fragmented opposition to the creation of a British state. So remove it, and many of the things that divided Highland opposition to Britain from Lowland opposition to Britain become very much more secondary. So maybe we get a GB of England, Wales and Ireland with a semi-detached Scotland? or not?